der Darsteller
actor
A person who plays a role in a film, a play, or a television program. A synonym is Schauspieler (actor).
Der Hauptdarsteller des Films hat einen Oscar gewonnen.
The lead actor in the film won an Oscar.

actor / representative
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actor
A person who plays a role in a film, a play, or a television program. A synonym is Schauspieler (actor).
Der Hauptdarsteller des Films hat einen Oscar gewonnen.
The lead actor in the film won an Oscar.

The word is derived from the verb 'darstellen' (to portray/represent), which means 'to show something' or 'to represent.' The ending '-er' denotes a male person, so a Darsteller is literally someone who portrays or represents something.
Er ist ein überzeugender Darsteller von komplizierten Charakteren.
He is a convincing actor of complicated characters.
In the context of film and theater, 'Darsteller' (actor) is often combined with other words. Common ones are 'Hauptdarsteller' (lead actor), 'Nebendarsteller' (supporting actor), and 'Laiendarsteller' (amateur actor).
Für die Rolle wurde ein bekannter Hauptdarsteller engagiert.
A well-known lead actor was hired for the role.
In the less common, figurative meaning, what the person represents is often specified. Pay attention to a genitive construction or the preposition 'von' (of), for example 'Darsteller eines bestimmten Lebensstils' (representative of a certain lifestyle).
Er galt als perfekter Darsteller des modernen, erfolgreichen Mannes.
He was considered the perfect representative of the modern, successful man.
representative / substitute
'der Vertreter' and 'der Darsteller' can both have to do with representation, but they are used differently. A 'Vertreter' acts for a person, group, or company, or stands as an example of a group. A 'Darsteller' presents something outwardly or embodies it; much more often, however, the word means someone who plays a role in film or theater. The risk of confusion arises because both words can sometimes mean 'to present or represent something'. For real action on someone's behalf, 'Vertreter' fits; for a role or an outward presentation, 'Darsteller' fits.

Der Darsteller wirkt in der Rolle des jungen Arztes sehr glaubwürdig.
The actor seems very convincing in the role of the young doctor.
Bei der Konferenz sprach ein Vertreter der Eltern über die Probleme in der Schule.
At the conference, a representative of the parents spoke about the problems at the school.